Lemma 3.7 [1]}
Let \((V,\rho )\)  be an algebraic irreducible representation of \(H\)  with the highest weight \(\chi \) . Then, there exists a \(K\) -invariant Euclidean norm \(\Vert .\Vert \)  on \(V\)  such that for every element \(a \in D\) , \(\rho (a)\)  is a symmetric endomorphism of \(V\) . Moreover, for every \(\eta \in H/P\) , non-zero \(v \in V_\eta \)  and \(h \in H\) , we have
\(\overline{\chi }(\overline{\sigma }(h,\eta ))=\log \frac{\Vert \rho (h)v\Vert }{\Vert v\Vert }.\) 

